MATHS 7101 - Multivariable and Complex Calculus
North Terrace Campus - Semester 1 - 2021
General Course Information
Course Code MATHS 7101 Course Multivariable and Complex Calculus Coordinating Unit School of Mathematical Sciences Term Semester 1 Level Postgraduate Coursework Location/s North Terrace Campus Units 3 Contact Up to 3.5 hours per week Available for Study Abroad and Exchange Y Assumed Knowledge MATHS 1012 Course Description The mathematics required to describe most "real life" systems involves functions of more than one variable, so the differential and integral calculus developed in a first course in Calculus must be extended to functions of more variables. In this course, the key results of one-variable calculus are extended to higher dimensions: differentiation, integration, and the link between them provided by the Fundamental Theorem of Calculus are all generalised. The machinery developed can be applied to another generalisation of one-variable Calculus, namely to complex calculus, and the course also provides an introduction to this subject. The material covered in this course forms the basis for mathematical analysis and application across an extremely broad range of areas, essential for anyone studying the hard sciences, engineering, or mathematical economics/finance.
Topics covered are: introduction to multivariable calculus; differentiation of scalar- and vector-valued functions; higher-order derivatives, extrema and Lagrange multipliers; integration over regions, volumes, paths and surfaces; Green's, Stokes' and Gauss's theorems; an introduction to complex numbers and functions; complex differentiation; complex integration and Cauchy's theorems.
Course Coordinator: Associate Professor Sanjeeva Balasuriya
The full timetable of all activities for this course can be accessed from Course Planner.
Course Learning Outcomes
- Demonstrate understanding of the basic concepts of calculus involving more than one real variable.
- Demonstrate understanding of the basic concepts of calculus for one complex variable.
- Be able to state and apply the major results in the course.
- Apply the theory in the course to solve a variety of problems at an appropriate level of difficulty.
- Demonstrate skills in communicating mathematics orally and in writing.
University Graduate Attributes
This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:
University Graduate Attribute Course Learning Outcome(s) Deep discipline knowledge
- informed and infused by cutting edge research, scaffolded throughout their program of studies
- acquired from personal interaction with research active educators, from year 1
- accredited or validated against national or international standards (for relevant programs)
all Critical thinking and problem solving
- steeped in research methods and rigor
- based on empirical evidence and the scientific approach to knowledge development
- demonstrated through appropriate and relevant assessment
all Teamwork and communication skills
- developed from, with, and via the SGDE
- honed through assessment and practice throughout the program of studies
- encouraged and valued in all aspects of learning
3 Career and leadership readiness
- technology savvy
- professional and, where relevant, fully accredited
- forward thinking and well informed
- tested and validated by work based experiences
5 Self-awareness and emotional intelligence
- a capacity for self-reflection and a willingness to engage in self-appraisal
- open to objective and constructive feedback from supervisors and peers
- able to negotiate difficult social situations, defuse conflict and engage positively in purposeful debate
- Textbook: Multivariable and Complex Calculus, Matt Finn and Sanjeeva Balasuriya, University of Adelaide (2021).
- Purpose built video lecture recordings for each section of the textbook.
- External videos relevant to the course material.
Online LearningThis course uses MyUni exclusively for providing electronic resources, such as the textbook, videoed lectures, tutorial questions, assignments, sample solutions, quizzes (for self-testing) discussion boards, sample test/examination etc. Students must make appropriate use of all these resources to succeed in this course.
Learning & Teaching Activities
Learning & Teaching ModesCourse delivery will occur on a weekly timetable. Each week typically consists of a variety of learning activities. All asynchronous activities/resources will be released at the beginning of each week, to enable students to personalise their schedules. Weekly tasks include:
- Reading the relevant sections of the textbook.
- Viewing video-recorded lecture material which complements rather than mimics the textbook.
- Participation in a synchronous scheduled (face-to-face or remote) tutorial session, which is designed for active learning.
- Attempting the extra practice problems which are released with the tutorial sheets.
- Reviewing whether the learning outcomes -- listed at the end of each relevant section in the textbook -- have been achieved.
- Completing a short online quiz to strengthen understanding of the relevant weekly material.
- Review released solutions from the previous week's tutorial questions.
- Attend the online consulting sessions as necessary, particularly if the student is having difficulty in achieving the learning outcomes.
The information below is provided as a guide to assist students in engaging appropriately with the course requirements.
Activity Quantity Workload Hours Engaging with the written (textbook) and oral/visual (lecture recordings) course material 88 Tutorials and Practice Problems 11 22 Quizzes 10 5 Assignments 5 10 Revising and studying 31 Total 156
Learning Activities SummaryThe learning activities are centred around the course content, given below in terms of the relevant chapters of the textbook:
- Functions of many variables: preliminaries
- Differentiation of multivariable functions
- Integration of multivariable functions
- Fundamental theorems of multivariable calculus
- Complex calculus
- Week 1: Course introduction, Section 1.1
- Week 2: Sections 1.2, 2.1
- Week 3: Sections 2.2, 2.3
- Week 4: Sections 2.4, 2.5
- Week 5: Sections 2.6, 3.1
- Week 6: Sections 3.2, 3.3
- Week 7: Section 3.4
- Week 8: Sections 3.5, 4.1
- Week 9: Sections 4.2, 4.3
- Week 10: Sections 5.1, 5.2
- Week 11: Sections 5.3, 5.4
- Week 12: Section 5.5
- Week 13: No new material, Course Review and Examination Preparation
Small Group Discovery ExperienceIn the tutorials.
The University's policy on Assessment for Coursework Programs is based on the following four principles:
- Assessment must encourage and reinforce learning.
- Assessment must enable robust and fair judgements about student performance.
- Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
- Assessment must maintain academic standards.
Assessment Task Type Due Weighting Learning Outcomes Final Examination Summative Final Examination period 40% All Mid-semester Test Summative and Formative Week 8 20% All Quizzes (10) Summative and Formative Weeks 2, 3, 4, 5, 6, 8, 9, 10, 11, 12 10% All Assignments (5) Summative and Formative Weeks 3, 5, 8, 10, 12 30% All
Assessment Item Distributed Due Weighting Quiz 1 Week 2 End of Week 2 1% Quiz 2 Week 3 End of Week 3 1% Quiz 3 Week 4 End of Week 4 1% Quiz 4 Week 5 End of Week 5 1% Quiz 5 Week 6 End of Week 6 1% Quiz 6 Week 8 End of Week 8 1% Quiz 7 Week 9 End of Week 9 1% Quiz 8 Week 10 End of Week 10 1% Quiz 9 Week 11 End of Week 11 1% Quiz 10 Week 12 End of Week 12 1% Assignment 1 Week 2 Week 3 6% Assignment 2 Week 4 Week 5 6% Assignment 3 Week 7 Week 8 6% Assignment 4 Week 9 Week 10 6% Assignment 5 Week 11 Week 12 6% Mid-semester Test Week 8 20%
All submissions are to be done using MyUni, following the relevant instructions. Submission deadline will be strictly adhered to.
- Any delay in assignment submissions will attract penalties.
- Quizzes not completed by the due time will not be accepted by the system.
- The Mid-semester Test must also be strictly completed by the due time.
Grades for your performance in this course will be awarded in accordance with the following scheme:
M10 (Coursework Mark Scheme) Grade Mark Description FNS Fail No Submission F 1-49 Fail P 50-64 Pass C 65-74 Credit D 75-84 Distinction HD 85-100 High Distinction CN Continuing NFE No Formal Examination RP Result Pending
Further details of the grades/results can be obtained from Examinations.
Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.
Final results for this course will be made available through Access Adelaide.
The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.
SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the University to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy (http://www.adelaide.edu.au/policies/101/) course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.
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